How tell if a big fraction can't be simplified more?

[mathstriker]

Hello there. I have been wondering is there a trick to tell if a big number fraction can be further simplified or not? Like how to tell if 1234/4356 is able to be simplified?

 

[MarkFL]

In the example you give, we can immediately see both the numerator and denominator are even, so they can both de divided by 2. In general, I would use a prime factorization on the two numbers to see what factors they may have in common.

[MATH]1234=2\cdot617[/MATH]
[MATH]4356=2^2\cdot3^2\cdot11^2[/MATH]
We see that 2 is the only factor the two numbers have in common.

 

[Dr.Peterson]

If you have very large numbers so that factoring completely is hard, you can find the GCF by the Euclidean algorithm, which requires only a series of divisions.

I'm assuming you aren't using a calculator; many calculators will do the simplification for you, if you ask them politely (and are allowed to).

 

[Steven G]

My response is that you should know the divisibility rules.

For example a number is divisible by 2 if the last digit is even.

A number is divisible by 3 if the sum of the digits is a multiple of 3.

A number is divisible by 4 if 4 goes into the two most right digits.

A number is divisible by 5 if the number ends in a 0 or a 5.

A number is divisible by 6 if it satisfies the rules for divisible by 3 and the rule for divisibly by 2.
....

Knowing these rule will be very helpful.

For example I know that 4356 is divisible by 3 since 4+3+5+6 = 18 and 18 is a multiple of 3. It also is a multiple of 2 since it ends in an even digit, namely 6. As a result of the above it is also divisible by 6.

Reducing is a game and to play the game you need to know the rules!